Heights of men on a baseball team have a bell-shaped distribution with a mean of 166 cm166 cm and a standard deviation of 6 cm6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values?a. 148148 cm and 184184 cm b. 160160 cm and 172172 cm

a) 89%; b) 68%

Step-by-step explanation:

We know that a mean and a standard deviation is

a) Notice that 148 and 184 are each exactly 3 standard deviation away from the mean:

So, we get that at least of the men has a height between 148 cm and 184 cm.

b) Notice that 160 and 172 are exactly 1 standard deviation away from the mean.

By the empirical rule , 68% of the men has a height between 160 cm and 172 cm.